Turkish Journal of Engineering and Environmental Sciences

Abstract: A 2-stage discrete-time linear quadratic reliable control technique is applied to the regulation of irrigation canals. The Saint-Venant equations of open-channel flow are linearized using the Taylor series and a finite difference approximation of the original nonlinear, partial differential equations. The concepts of linear optimal control theory are applied to derive a feedback control algorithm for constant level control of an irrigation canal. Two-step linear quadratic update equations and a sequential gain updating scheme are used to drive a linear quadratic reliable formulation. An example problem with a single pool is considered for evaluating the performance of the reliable control technique used to design an optimal control for irrigation canals. The results from the 2-stage reliable control technique are compared to the results from a standard linear quadratic regulator (LQR). The 2-stage reliable control formulation provides both good stability and performance gain margins in the canal operation. The results of this study show that a 2-stage linear quadratic reliable control for irrigation canals offers an alternative to the standard optimal control formulation if there is a lack of flow depth and flow rate data at some measurement points in the irrigation canal.

Key Words: Irrigation canals, Two-stage reliable control, Linear quadratic control.